Question: Simplify the following expression: $\sqrt{44}+\sqrt{99}+\sqrt{176}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{44}+\sqrt{99}+\sqrt{176}$ $= \sqrt{4 \cdot 11}+\sqrt{9 \cdot 11}+\sqrt{16 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{11}+\sqrt{9} \cdot \sqrt{11}+\sqrt{16} \cdot \sqrt{11}$ $= 2\sqrt{11}+3\sqrt{11}+4\sqrt{11}$ Finally, simplify by combining the terms. $= ( 2 + 3 + 4 )\sqrt{11} = 9\sqrt{11}$